Large enhancement of KK dark matter annihilation rate due to threshold singularity

1. Large enhancement of KK dark matter annihilation ratedue to threshold singularity Mitsuru Kakizaki (ICRR, University of Tokyo) Dec. 2004 @ Stanford Univ. • Collaborated with Shigeki Matsumoto and Masato Senami (ICRR), in preparation • Kaluza-Klein (KK) dark matter annihilation cross section is significantly enhanced due to the threshold singularity in the non-relativistic (NR) limit

2. １．Motivation • Rotation curve of galaxies: [Begeman, Broeils, Sanders, (1991)] • Mass-to-light ratio of galaxy clusters: e.g. the Coma cluster: • Cosmic microwave background anisotropies: [http://map.gsfc.nasa.gov] Existence of non-baryonic cold dark matter (CDM)

3. What is the constituent of dark matter? • We need physics beyond the standard model (SM) • Candidates: • Lightest supersymmetric (SUSY) particle (LSP) e.g. Neutralino, gravitino • Lightest Kaluza-Klein particle (LKP) in universal extra dimensions • etc. Today’s topic

4. How to detect • Direct detection • Indirect detection: • Positrons from annihilations in the galactic halo • Antiprotons • Exotic gamma rays from the galactic center • Neutrinos from the sun and earth Today’s topic

5. DM DM Positron detection The milky way • In the neighborhood of our solar system: (Almost at rest) Dark matter halo Primary is monoenergetic: • signal is broadened during propagation: Flux

6. Positron experiments • The HEAT experiment indicated an excess in the positron flux: • Unnatural dark matter substructure is required to match the HEAT data in SUSY models [Hooper, Taylor, Kribs (2004)] • KK dark matter can explain the excess [Hooper, Kribs (2004)] • Future experiments (PAMELA, AMS-02, …) will confirm or exclude the positron excess

7. Purpose • Reconsideration of pair annihilation processes of dark matter in universal extra dimensions (UED), in which all the SM fields propagate • The 1st excited mode of boson, , is CDM candidate • is almost degenerate with other first KK modes • The annihilation cross section is enhanced due to the threshold singularity in the non-relativistic limit. • Predicted flux can be increased compared with that at the tree level. [c.f. Cheng, Feng, Matchev (2002)]

8. Contents Motivation Universal extra dimension (UED) Annihilation cross section of KK dark matter Threshold cross section in the NR limit Summary New

9. 2. Universal extra dimension Idea: All SM particles propagate spatial extra dimensions [Appelquist, Cheng, Dobrescu] • For simplicity, we consider one extra dimension: • Eq. of motion: Mass spectrum in 4-dim. viewpoint • Momentum conservation in higher dim. Conservation of KK number

10. orbifold provides CDM • To obtain chiral fermions at zero mode, we identify with • Electroweak precision measurements restrict the size : • Conservation of KK parity [+ (--) for even (odd) ] The lightest KK particle (LKP) is stable LKP is a good candidate of cold dark matter c.f. R-parity and LSP in SUSY models

11. Mass spectra of KK states • Fourier expanded modes are degenerate in mass at each KK level 1-loop corrected mass spectrum of the first KK level • Radiative corrections remove the degeneracy • is the LKP and nearly degenerate with SU(2)L singlet • We treat the mass deference as a free parameter [From Cheng, Matchev, Schmaltz, PRD 036005 (2002)]

12. 3. Annihilation cross section of KK dark matter • We concentrate on mode: Annihilation cross section: [Cheng, Feng, Matchev (2002)] Bosonic property of the LKP avoids chirality suppression

13. . . . + + + New 4. Threshold cross section in the NR limit • is almost at rest and in internal lines are almost on-shell when their mass difference is tiny: Ladder diagrams can give dominant contributions Higher order calculations are important

14. Strategy 5-dim. UED action Effective action for and Non-relativistic approximation using NRQED method Eq. of motion of pair and pair Exactannihilation cross section for = Shroedinger equation The optical theorem

15. Derivation of effective action for and • 5-dimensional UED action: Fourier transform 4-dimensional action with KK particles • The relevant part for our calculation:Photon ( ), electron ( ), 1st-excited boson ( ) and electrons ( ), and their interactions Integrate out Effective action for and

16. Non-relativistic approximation On-shell • Definition of non-relativistic field: Particle NR region: Anti-particle • Non-relativistic :

17. Non-relativistic action Kinetic terms (electron exchange) Coulomb potential generated by exchange Imaginary part leading to annihilation:

18. 2-body effective action • Let us replace by composite fields: • Introduce auxiliary fields: : state of pair : Center-of-mass coordinate : Relative distance 2-body effective action: • Integrate fields out Coulomb, centrifugal force exchange

19. NR pair annihilation cross section for • The eq. of motion is the Shroedinger equation: We can treat non-perturtatively The optical theorem • The exact annihilation cross section: • Perturbative expansion of leads to usual loop expansion

20. Numerical result for The annihilation cross section is significantly enhanced when and are degenerate

21. 4. Summary • UED models provide a viable CDM candidate: The lightest Kaluza-Klein particle (LKP) • LKP is naturally degenerate with other first KK modes in mass KK dark matter annihilation cross section is significantly enhanced due to the threshold singularity in the NR limit, compared with that at the tree level

22. Future direction This work is now in progress • Inclusion of other imaginary parts in potentials • Consideration on effects caused by KK quarks and gluon mediated diagrams • Re-estimation of the positron flux • Investigation of annihilation cross sections to photons [c.f. Bergstroem, Bringmann, Eriksson, Gustafsson (2004)]

23. Backup slides

24. Inclusion of